Precalculus Examples

,
Step 1
Subtract from both sides of the equation.
Step 2
Replace all occurrences of with in each equation.
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Replace all occurrences of in with .
Simplify the left side.
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Simplify .
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Simplify each term.
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Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Move .
Multiply by .
Multiply by .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Add and .
Step 3
Solve for in .
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Subtract from both sides of the equation.
Subtract from .
Factor the left side of the equation.
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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Let . Substitute for all occurrences of .
Factor by grouping.
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Reorder terms.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Factor.
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Replace all occurrences of with .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
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Set equal to .
Solve for .
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Add to both sides of the equation.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Set equal to and solve for .
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Set equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
Step 4
Replace all occurrences of with in each equation.
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Replace all occurrences of in with .
Simplify the right side.
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Simplify .
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To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Step 5
Replace all occurrences of with in each equation.
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Replace all occurrences of in with .
Simplify the right side.
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Simplify .
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Multiply by .
Subtract from .
Step 6
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 7
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 8
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